Prehistoric numbers: What, when, and why (original) (raw)
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From number sense to number symbols. An archaeological perspective
Philosophical Transactions of the Royal Society B, 2017
How and when did hominins move from the numerical cognition that we share with the rest of the animal world to number symbols? Objects with sequential markings have been used to store and retrieve numerical information since the beginning of the European Upper Palaeolithic (42 ka). An increase in the number of markings and complexity of coding is observed towards the end of this period. The application of new analytical techniques to a 44–42 ka old notched baboon fibula from Border Cave, South Africa, shows that notches were added to this bone at different times, suggesting that devices to store numerical information were in use before the Upper Palaeolithic. Analysis of a set of incisions on a 72–60 ka old hyena femur from the Les Pradelles Mousterian site, France, indicates, by comparison with markings produced by modern subjects under similar constraints, that the incisions on the Les Pradelles bone may have been produced to record, in a single session, homologous units of numeri...
2022 - Numeracy at the dawn of writing: Mesopotamia and beyond
Historia Mathematica, 2022
Numeracy and writing constitute different phenomena, whose paths of formation often appear intertwined. Here we reassess the theory that numeracy evolved universally from a concrete to an abstract concept of number, and that that shift is correlated with the invention of writing. First, we gather contemporary linguistic data and early Mesopotamian epigraphic evidence that indicates that the ‘concrete’ vs. ‘abstract’ dichotomy is not useful to understand the emergence of numbers. Then, we discuss evidence from other regions where writing was probably invented independently, in order to investigate the conceptualization and formation of early numerical notations.
Numerical notations are virtually unknown for the Early Iron Age Greek world. However, it can be argued that different systems to write down numbers were already in use at that time. Many marks incised on vases might be related to such a practice. After a few methodological remarks on this issue, the paper focuses on the Euboean sphere (Eretria, Methone, Pithekoussai), where the existence of a coherent numeral system is hypothesised. Then the idea of a link between Euboean and Etruscan numerical notations, already put forward almost fifty years ago, is considered anew.
Six Unresolved Questions in the Early History of Numeration
Signs of Writing: The Cultural, Social, and Linguistic Contexts of the World’s First Writing Systems, 2014
Across multiple disciplines, written numerical notation is a topic of keen interest, yet several unresolved issues in its analysis are either elided or taken as settled. Numerical notation is a complex phenomenon with multiple independent histories—more than 100 distinct systems used over the past 5,500 years, interweaving with, rather than strictly paralleling, the histories of writing systems. Social, semiotic, and cognitive approaches are brought to bear on six incompletely answered questions about numeration in relation to the earliest writing. Is numerical notation a necessary precursor to writing? Does the earliest numerical notation initially serve a bookkeeping function for early states? What is the relationship between tallying and numerical notation? Does the use of numerical notation change human cognition about the domain of number? How does the emergence of numerical notation relate to linguistic representations of number? Finally, among all domains of knowledge, why is number so widely represented using graphic notations? Recognizing that these issues are not resolved, and identifying different possible resolutions, must be preliminary to fully integrating numerical notation within the broader history of writing.